Novel devices consisting of uniform-waist tapered optical fibers with asymmetric double-layer (metal plus dielectric) depositions have been recently proposed as refractive-index sensors. We study the properties of light transmission by use of this kind of devices, and we specifically perform a detailed study of the generation of surface-plasma waves in the structures. We show that multiple surface plasmons are excited for specific combinations of the constructive parameters of the devices and for specific ranges of the refractive index of the surrounding medium. The behavior also depends on the wavelength and the state of polarization of the incident light. The use of uniform-waist tapers allows for control of constructive parameters and an increase in the interaction length with the outer medium. We show how the plasmons are excited in the region of the taper waist by a coupling with the cladding modes guided in that area. This characterization shows the importance of the presence of a dielectric layer for selection of the operating range of the device. The results are useful for the design of new sensors.